Don't Ask, Don't Tell

The title I've chosen for this post could have been the title of a short recent piece by self-described "worker bee" economist Kartik Athreya. (The article, titled "Economics is Hard. Don't Let Bloggers Tell You Otherwise" may be accessed by contacting Athreya at the Richmond Fed.) Economics is hard, says Athreya. Well, yes. So what follows from that? Only Athreya seems to know. He has directed his short article, not to bloggers or economists, but to consumers of economics blogs. I wonder if he understands that the main way consumers of blogs would find out about his article criticizing economics blogs is by reading . . . economics blogs. OK, so that's a paradox rather than a contradiction. If a guy's going to reach people, he needs to use existing media even if he disapproves of these media, right? I'll grant him that. After all, I'm not a big fan of the New York Times, but I had a piece published in it.

But there are some bigger problems. Scott Sumner, in the best comment I have read on Athreya, has mentioned a few of them. Here's my take that, in some ways, overlaps Sumner's.

Athreya's apparent message is that bloggers should leave the heavy lifting of economics to the people who have had at least a year in a Ph.D. program at a "decent" economics department such as the University of Iowa. What are the important things that bloggers are leaving out? Mathematics. Athreya, in this short video [click on his], tells us that mathematics is the language of economics. Not one of the languages, which I'll grant him. The language.

What are the important issues that bloggers are getting wrong and that they would be more likely to get right if they had had a year in a "decent" economics program? He doesn't say. Nowhere in the piece does Athreya say anything like, "Here's what the bloggers are getting wrong, and here's where some careful analytic thinking by economists can get it right." No. It makes sense that he wouldn't give an example. After having told us that mathematics is the language of economics, and after having stood, in a video apparently aimed at the public, in front of a blackboard of mathematical spaghetti, there appears to be nothing he can add that non-economist consumers of blogs would understand.

Athreya's piece read like something from a newly minted PhD (though I know he is not) frustrated after his first year of undergraduate teaching. Really good professors are those who once used that frustration to learn - from students - not just how to teach but also to learn their discipline on a much richer level. Mediocre (or poor) professors stay stuck in PhD Land, always holding onto a little contempt for their students and everyone else not as specially educated as them.

It was actually surprisingly sophomoric.

None of that means there aren't bloggers out there with ridiculous economic thinking.

Certainly mathmatics is an important tool for economics. But sometimes the parameters that mathmatics work in need to be reconsidered, before math can do its important work. After studying economics for five years, I realized I needed to go back and really learn math so as to study economics seriously. But after making good grades in remedial math for two semesters, I realized that, at age 55, I was forgetting too quickly what had been learned the previous semester.

Economics needs help in the present. People like myself of course need to continue studying math, but that should not stop us from working with the knowledge we already worked and researched for, to add to the existing dialogue. It's too important now, not to.

If mathematics were useful or necessary for discussing economics, then one would expect that all economists would agree with each other once whatever mathematical equations were solved or mathematical proofs were constructed. That is usually how math works, but this is not what we see. Economists with PhDs, and presumably the requisite math skills, do not agree with each other about the meaning and significance of whatever sets of economic data, nor what to do to remedy specific problems in the economy - e.g. increasing state spending vs. cutting state spending. Does the math help economists to understand the world, or merely to discuss it intelligently?

For the record, I am not an economist. I come from the world of engineering, where the math seems simple (to me) by comparison. Also we can build prototypes and beta versions of things before letting them loose on the real world. Economists don't have this luxury.

Certainly math is overemphasized as an analytical tool in economics, but that's just the way it is. As a student begining a PhD program, I will have to jump through hoops my first two years. After that I'll use math when appropriate and some other technique when math isn't helpful. I guess you could say my objective function is to maximize clarity subject to the constraint of maintaing academic employment. The first order conditions are...
just kidding

@Thomas,
Could be. If so, it worked. I don't know the man so I can't say.
@MJOakes,
I agree with your point that many bloggers engage in ridiculous economic thinking. In that respect, the blogging world isn't that different from much of the rest of the world. As I tell my students, keep the wheat and throw out the chaff.
@Mounir,
Thanks.
@Rebecca Burlingame,
Good point and I appreciate your persistence.
@stuhlmann,
Very good point.
@Rob,
That's the sad truth. The number of really promising economics students I've run into over the years in economics who can't hack the math or don't want to hack the math cannot be counted on all my fingers and all my toes.

Of what use is using mathematics in economics if the results cannot be translated back into plain English? How can anyone really understand something that they cannot describe without using numbers and equations?

A quote from Marshall:
"But I know I had a growing feeling in the later years of my work on the subject that a good mathematical theorem dealing with economic hypotheses was very unlikely to be good economics: and I went more and more on the rules-(1) Use mathematics as a shorthand language, rather than an engine of enquiry. (2) Keep to them till you know you are done. (3) Translate into English. (4) Then illustrate by examples that are important in real life. (5) Burn the mathematics. (6) If you cannot succeed in 4, burn 3. This last I did often."

But after making good grades in remedial math for two semesters, I realized that, at age 55, I was forgetting too quickly what had been learned the previous semester.

Don't misunderstand the nature of this beast. Nobody "remembers" math until they've had to actually use it for something.

Go find a class that actually uses the math you just learned. You may think you're having to re-learn the math you already learned but in fact, you're probably learning anew at a deeper level.

I'm a PhD engineer and physics comes to mind as a good course to give you math practice. But that may not be worth much to an economist.

In any case, I found math much easier to both learn and remember, once I had to actually do something with it. I believe this is true for many, perhaps most people*.

*Disclaimer: there is a small percentage of the population whose brains seem to just naturally "think math". Curiously, many of them I've known told me that they had a lot of trouble with courses that actually use math. ?? For me, and many others I've known, it's just the opposite.

Don't give up and don't sell yourself short. Even with a PhD in engineering, when I have to go learn new math today it's still hard work.

What are the important things that bloggers are leaving out? Mathematics.

I don't believe it. This from me, who derives my own partial differential equations from first principles physics on a routine basis.

When you start dealing with complex systems, the precision that mathematics entails by nature is its biggest limitation. It leads one to believe that the problem is better understood (and quantified, in your equations) than in fact it really is.

It's those evil color graphs that you stick on power point slides that really leads people astray. :)

Math is a tool. But gut instinct tells me it's not as central to economics as it is to engineering. Because, for one thing, it's too hard to quantify or test the validity of the generalizations that go into deriving the governing equations.

Plus economics has to be full of mathematical singularities. You can project the future of the horse shoe making industry, but how do you put Henry Ford into that equation? How do you even know that you need to put Henry Ford in the equation?

On the topic of maths in economics, I think the useful thing about using maths is that it forces a clarity about what you are saying. Quite often I've come across people who say something about how people should optimally behave, when it strikes me as very doubtful that such behaviour is optimal. One striking example was an article on the Indian caste system, where certain castes could not do some work for themselves such as cleaning up garbage, and thus hired lower-caste people to do this. The author asserted that being unable to do some work yourself improved your bargaining position, which rather flew in the face of everything I know about negotiating positions. A bit more rigorous approach might have made that problem obvious to him.

Another problem is forgetting to account for the system-wide effects of actions, for example if people buy gold to hedge against inflation, then obviously there must be someone selling gold and thus becoming unhedged against inflation.

The areas where economists most disagree are in macroeconomics, where no mathematical model can obviously capture the full complexity of the economy, and in those areas where theory tells us there is no one clear result (eg effect of taxes on labour supply), or it's a question of conflicting values or different views about the future. Where mathematic models are clear, eg comparative advantage, I don't know of any economists who disagree, although they may disagree about the policy implications.

I came to economics from electrical engineering, so my comfort level with the maths is higher than most people's.

the precision that mathematics entails by nature is its biggest limitation. It leads one to believe that the problem is better understood (and quantified, in your equations) than in fact it really is...

This is not my experience. In my experience people are entirely capable of being ridiculously overconfident when confined to words only. For example, those people who don't consider that every buyer must mean a seller.

Math is a tool. But gut instinct tells me it's not as central to economics as it is to engineering. Because, for one thing, it's too hard to quantify or test the validity of the generalizations that go into deriving the governing equations.

But with language, it's even harder to figure out what your generalisations are. Or what your governing equations are. So, one method you find it hard to quantify or test the validity, the other method you find it hard to know what you're talking about at all.

You can project the future of the horse shoe making industry, but how do you put Henry Ford into that equation? How do you even know that you need to put Henry Ford in the equation?

Because you built a neoclassical growth model that did not assume any innovation, and then tried to match the results with real world data and realised you missed something? Or you started off with your knowledge of the real world, which included Henry Ford, and decided that you needed to build a model which included him?

Let's take electrical engineering. How do you know when you need to use Maxwell's Equations or when you can get away with just using Kirchoff's Laws? There's two ways I know of. One is that you start off with your knowledge of the real world and realise that you need to use Maxwell's Equations (eg the frequency of your CPU means that the wavelength is shorter than the motherboard you are designing), or you build your model and realise that it doesn't explain reality well enough. Am I missing some way of figuring out that the model doesn't match with reality?

I think you are expecting too much of mathematics here. It's not necesary for mathematics to solve all of economics' problems for it to be useful, it's only necessary that mathematics be more useful than doing without mathematics.

I'm not saying math isn't useful in economics. I am saying, some writers I've read, seem way too confident in the results of their mathematical models for my blood.

I've worked on Maxwell's equations a time or two myself. The issue comes down to identifying the time and length scales relevant to the problem at hand, in order to figure out whether you need the full blown transient case, or whether simplifications are close enough.

But Henry Ford doesn't show up in Maxwell's equations and you don't have to try and include some term for "innovation". My point here is that, "innovation" is an utter unknown until after the fact.

Which means economics equations -- though I grant they have value -- are limited in their predictive power. Akin to saying in a controls problem, that we may not have a causal system.

Which doesn't change the fact that an "all other things being equal" kind of economic analysis, using all kinds of mathematics, can't be of great value. I agree that it can.

Just don't bet the whole farm on the results. You never know when that Henry Ford term is going to blow up on you. :)

MernaMoose - I agree with you that some people are way too confident in the results of their mathematics. My observation continues to be that that I think that more people are way too confident in the results of their language-only thinking.

I don't understand what point you are trying to make when you say that Henry Ford's innovations don't show up in Maxwell's Equations. Maxwell's Equations are about electromagnetic field theory, they're not a universal explanation of everything in physics, chemistry and biology, let alone the whole social sciences. Maxwell's Equations are hard enough as they are just accounting for electromagnetic field effects.

I agree with you that economics equations have limited predictive power. I actually work as a forecaster, I am well aware of how often I get things wrong. And in my experience, the people who hire forecasters are also well aware of how often we get things wrong. Why do people keep hiring forecasters, and why do I work as one, despite that "everyone" knows that forecasting is often wrong? Because we have to make decisions about the future, and none of the critics of forecasting have come up with any better solution. Take Nassim Taleb, whose book The Black Swan is sitting on my desk at the moment. He says his advice is not to forecast, but how do you decide whether or not to build another power plant, or a printing press, or a school building, or what degree to do, without forming opinions about the future? We might be wrong in our forecasts, I am in favour of scenario planning (why wouldn't I be? Instead of selling one forecast, I can sell 3, or 5!), but, risk is a part of life. Wild animals don't do any mathematics, as far as we can tell, and yet they run risks just getting food and water and mates, and in terms of life expectancy do far worse on average than us humans with our mathematics. The only way to avoid running risks is to be dead. I prefer running risks. I might fail, but hey, the risk-free way I definitely fail.

Dr Athreya has missed an important point: Economists know Economics. They don't necessarily know anything about the economy. (Consult the table of contents of any econ journal. See if you can find ANY articles that deal with the actual economy.) Search for even one cluster of economists or school of economics that anticipated the current meltdown.

I'm an engineer who heard radio advertisements suborning the fraudulent mortgage applications in 2007. I knew that borrower fraud must eventually be fraud against borrowers but I never heard or read any economists who recognized that fact or its consequences.

At Milton Friedman's 90th birthday party, Ben Bernanke delivered an oration that was IMO a cogent argument against central banking. He said that the Fed caused the Great Depression I. He scorned his predecessors of the 1920s for not recognizing the fragile financial structure of their day. I wondered as I read the speech if Dr. Bernanke knew anything worthwhile about the financial structure of the time in which he lived. Indeed, in retrospect, did any economists?

I plan to continue asking and telling in spite of my lack of a PhD in Econ.

I have to disagree. My background is in physics, where math is quite clearly "the language" and frequently people still disagree. They do not disagree over the question of whether the math is correct as such. If it is logically incorrect all involved will eventually (though even that can take a long time to discern) agree that some error in logic or calculation renders the mathematical formalization invalid.

What they do disagree on is the application of the equations to the real world. It's one thing to see Einstein's field equations and verify that he did the math correctly, and it is another to determine that the math accurately described the relative nature of space and time in our actual universe. It's one thing to verify the math suggesting that particles can exist in a superposition of various (mutually exclusive) states, and another to believe that a single particle in the real world actually behaves that way. Both were very controversial, and requires empirical evidence before they were widely accepted.

Even in pure math, it's not always so simple. There was a crisis in the formulation of set theory a hundred years ago. Georg Cantor had a breakdown over the amount of controversy his work generated and the fights that ensued.

Bill Drissel, why do you say that the table of contents don't deal with the actual economy? Every economics journal I have ever read deals with the actual economy. Look at the latest edition of the American Economic Review. Article titles include:
The Macroeconomic Effects of Tax Changes: Estimates Based on a New Measure of Fiscal Shocks

Is a Donor in Hand Better Than Two in the Bush? Evidence from a Natural Field Experiment

Trade Shocks and Labor Adjustment: A Structural Empirical Approach

Investment and Usage of New Technologies: Evidence from a Shared ATM Network

All these are articles that deal with the actual economy, from their title. Indeed, the typical bog-standard economic article consists of proposing a model in the first part of the paper and empirically testing it in the second.

I knew that borrower fraud must eventually be fraud against borrowers but I never heard or read any economists who recognized that fact or its consequences.

McCarthy, Jonathan and Peach, Richard W., Are Home Prices the Next Bubble?. Economic Policy Review, Vol. 10, No. 3, December 2004. Available at SSRN: http://ssrn.com/abstract=634265

This is, I find, typical of many critics of economists, they feel free to just make up false assertions about the state of economics, even though about 5 minutes with Google would have provided ample evidence that their claims were wrong.

Here are the first two sentences of the abstracts from the latest issue of American Economic Journal: Microeconomics: Readers can form their own opinions of how much of this has anything to do with the real economy.

"We develop a theory of firm scope and structure in which merging two firms allows the integrated firm's top management to allocate resources that are costly to trade. However, information about their use resides with division managers.

"This paper explores information disclosure in matching markets. A school may suppress some information about students in order to improve their average job placement.

"In our model, production of a final good requires access to an excludable resource owned by an integrated firm. The quality of the resource depends on an investment by the owner and impacts the downstream demand curve.

"I consider a uniform-price auction under complete information. The possibility of resale attracts speculators who have no use value for the objects on sale.

"We introduce new revelation mechanisms for simultaneous common agency games which, although they do not always permit a complete equilibrium characterization, do facilitate the characterization of the equilibrium outcomes that are typically of interest in applications. We then show how these mechanisms can be used in applications such as menu auctions, competition in nonlinear tariffs, and moral hazard settings.

"We model privacy as an agent's choice of action being unobservable to others. An agent derives utility from his action, the aggregate of agents' actions, and other agents' perceptions of his type.

"More and more academic journals are adopting an open access policy by which articles are accessible free of charge, while publication costs are recovered through author fees. We study the consequences of this open access policy on the quality standard of an electronic academic journal.

Bill, most of these strike me as being about the real economy.
- Firm mergers, these do happen in the real econonmy. And inside a firm, the top level managers typically do know different things to the division managers.
- Do you think that in the real economy, everyone tells all the relevant truth, and, say, schools don't have any incentive to suppress some information about students?
- Do you really think that in the real economy, tariff setting is not an economic issue? So, for example, whatever tariffs state regulators might set doesn't matter for either static or dynamic issues?
- Do you really think that real world economies don't involve auctions?
- This abstract lost me. Don't know if that's a reflection of their writing skills or my ignorance.
- Do you really think that people's inclination to contribute to public goods, in the economic sense, has nothing to do with how they think others will perceive their contribution?
- Pricing of academic journals, I'll give you this one as a matter of interest only to economists.

Judging by your selection of these articles, I guess that you think that in the real economy, firms never merge, or at least that firm mergers always create shareholder value, organisations never have an incentive to be selective about the truth, tariffs (and thus the prices people pay for goods or services) have no affect on anything economic, people don't care about how others perceive them when it comes to public-spiritedness, and no one ever holds auctions.

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